A Panorama of Hungarian Mathematics in the Twentieth Century, I

Cover......Page 1
Bolyai Society Mathematical Studies Volume 14......Page 3
A Panorama of Hungarian Mathematics in the Twentieth Century I......Page 4
3540289453......Page 5
Table of Contents......Page 8
PREFACE......Page 10
TOPOLOGY......Page 12
REFERENCES......Page 26
Constructive Function Theory......Page 30
1. THE RIESZ-FISCHER THEOREM......Page 32
2. RIESZ TYPICAL MEANS......Page 36
3. T HE HAAR ORTHOGONAL SYSTEM......Page 39
4. THE SATURATION PROBLEM FOR THE FEJER MEANS......Page 42
5. ALMOST EVERYWHERE CONVERGENCE OF ORTHOGONAL SERIES......Page 46
6. CESARO SUMMABILITY OF ORTHOGONAL SERIES......Page 52
7. UNCONDITIONAL CONVERGENCE OF ORTHOGONAL SERIES......Page 54
REFERENCES......Page 55
ORTHOGONAL POLYNOMIALS......Page 58
REFERENCES......Page 72
1. INTRODUCTION......Page 74
2. LAGRANGE INTERPOLATION. LEBESGUE FUNCTION. LEBESGUE CONSTANT. OPTIMAL LEBESGUE CONSTANT. DIVERGENCE OF INTERPOLATION......Page 75
3. ON THE CONVERGENCE OF THE INTERPOLATORY PROCESSES......Page 87
4. HERMITE-FEJER TYPE AND OTHER CONVERGENT INTERPOLATORY PROCESSES......Page 90
5. LACUNARY OR BIRKHOFF INTERPOLATION......Page 96
6. ON THE MEAN CONVERGENCE OF INTERPOLATION......Page 100
7. WEIGHTED LAGRANGE INTERPOLATION , WEIGHTED LEBESGUE FUNCTION, WEIGHTED LEBESGUE CONSTANT......Page 105
8. GETTING CONVERGENCE BY RAISING THE DEGREE......Page 110
9. MEAN CONVERGENCE......Page 111
REFERENCES......Page 112
1. MARKOV- AND BERNSTEIN-TYPE INEQUALITIES......Page 122
2. MUNTZ POLYNOMIALS AND EXPONENTIAL SUMS......Page 130
3. GEOMETRIC PROPERTIES OF POLYNOMIALS......Page 136
REFERENCES......Page 154
Harmonic Analysis......Page 160
1. THE THEOREM OF FEJER......Page 162
2. THE THEOREM OF RIESZ-FISCHER......Page 169
3. BOUNDARY VALUES OF ANALYTIC FUNCTIONS......Page 174
4. RIESZ PRODUCT AND SIDON SETS......Page 178
5. MISCELLANEOUS*......Page 182
REFERENCES......Page 191
NON-COMMUTATIVE HARMONIC ANALYSIS......Page 196
1.2. Invariant Measures a nd Analysis on Locally Compact Groups......Page 197
1.3. Representation Theory and Quantum Physics......Page 199
1.4 . Invariant Means and Almost Periodic Functions and Groups......Page 201
1.5. Von Neumann Algebras......Page 203
1.6. Development of Unitary Representation Theory of Non-Compact Lie Groups......Page 205
2.1. Bela Sz.-Nagy......Page 207
2.2. Lajos Pukanszky......Page 208
REFERENCES......Page 210
A PANORAMA OF THE HUNGARIAN REAL AND FUNCTIONAL ANALYSIS IN THE 20TH CENTURY......Page 214
REFERENCES......Page 243
Summary.......Page 248
At the turn of the century.......Page 249
Lajos Schlesinger and his work.......Page 250
Fejer summation theorem and the Dirichlet problem on the unit disc.......Page 252
The work of Fejer in mechanics and his habilitation lecture.......Page 253
F. Riesz' subharmonic functions.......Page 256
The works of F. Riesz and Haar on linear integral equations.......Page 257
Haar's inequality for partial equations of the first order.......Page 258
Haar's existence and uniqueness theorem in the calculus of variations.......Page 259
T. Rado's regularity Lemma.......Page 261
Haar's Lemma on the variation of double integrals.......Page 262
An early paper on billiards.......Page 264
Neumann's method of stability analysis.......Page 265
Lax equivalence theorem, the theoretical result behind.......Page 269
The work of Lax on a single conservation law.......Page 270
The work of Lax on systems of conservation laws......Page 273
The Lax-Milgr am Lemma......Page 274
A cross-section in 1928. The state of art.......Page 275
Polya and Szego on isoperimetric inequalities.......Page 276
M. Riesz' fractional potentials.......Page 280
The work of Egervary.......Page 282
A cross-section in 1953. The state of art.......Page 284
Bihari inequality.......Page 285
The contributions of Makai.......Page 287
Epilogue......Page 291
REFERENCES......Page 292
2. THE JENSEN FORMULA......Page 298
3. POLYNOMIALS......Page 300
4. TRIGONOMETRIC POLYNOMIALS, TOEPLITZ FORMS AND A PROBLEM OF CARATHEODORY......Page 309
5. THE FEJER-RIESZ INEQUALITY......Page 319
6. BOUNDARY VALUES, HP SPACES......Page 321
7. KAKEYA'S THEOREM, POWER SERIES WITH MONOTONE COEFFICIENTS......Page 326
8. POWER SERIES: SINGULARITIES AND ANALYTIC CONTINUATION......Page 337
9. TURAN'S "NEW METHOD"......Page 350
10. POWER SERIES: BEHAVIOR ON THE CIRCLE OF CONVERGENCE......Page 354
11. POLYA-SCHUR FUNCTIONS......Page 358
12. CONFORMAL MAPPING, COMPLEX INTERPOLATION......Page 367
REFERENCES......Page 372
THEODORE VON KARMAN......Page 376
The von Karman equations for plates.......Page 377
The von Karman vortex street.......Page 379
Mathematical methods in engineering.......Page 380
Aeronautics and astronautics.......Page 381
REFERENCES......Page 382
Geometry......Page 386
DIFFERENTIAL GEOMETRY......Page 388
REFERENCES......Page 413
1. INTRODUCTION......Page 418
2. THE PROBLEM OF MOTION......Page 419
3. THE LANCZOS POTENTIAL......Page 422
4. THE LORENTZIAN SIGNATURE......Page 423
REFERENCES......Page 427
1. INTRODUCTION......Page 430
2. THE BEGINNINGS......Page 431
3. PACKINGS AND COVERINGS BY CIRCLES......Page 434
4. PACKINGS AND COVERINGS BY INCONGRUENT CIRCLES......Page 435
5. PACKINGS AND COVERINGS BY CONVEX SETS IN THE PLANE......Page 436
6. PACKINGS AND COVERINGS ON THE SPHERE......Page 438
7. PACKINGS AND COVERINGS IN THE HYPERBOLIC PLANE......Page 440
8. PACKINGS AND COVERINGS IN HIGHER DIMENSIONS......Page 441
9. APPROXIMATION......Page 442
10. THE ERDOS-SZEKERES THEOREM......Page 443
11. REPEATED DISTANCES, DISTINCT DISTANCES IN THE PLANE......Page 445
12. REPEATED AND DISTINCT DISTANCES ELSEWHERE......Page 447
13. INCIDENCES......Page 448
14. MISCELLANEOUS RESULTS IN COMBINATORIAL GEOMETRY......Page 450
15. FINITE GEOMETRIES......Page 452
16. STOCHASTIC GEOMETRY......Page 453
17. MISCELLANEOUS RESULTS IN CONVEX GEOMETRY......Page 454
REFERENCES......Page 457
Stochastics......Page 458
PROBABILITY THEORY......Page 460
REFERENCES......Page 488
1. INTRODUCTION......Page 494
2. EARLY STATISTICS IN HUNGARY......Page 495
3. SEQUENTIAL ANALYSIS......Page 499
4. STATISTICAL DECISION FUNCTIONS......Page 501
5. ASYMPTOTIC THEORY OF TESTING AND ESTIMATION......Page 503
6. RANDOMNESS......Page 504
7. NONPARAMETRIC TESTS, ORDER STATISTICS......Page 505
8. GOODNESS OF FIT TESTS......Page 514
9. CRAMER-FRECHET-RAO INEQUALITY......Page 517
REFERENCES......Page 519
STOCHASTICS: INFORMATION THEORY......Page 526
INFORMATION THEORY IN HUNGARY......Page 527
DIMENSIONAL ENTROPY......Page 528
RENYI INFORMATIONS......Page 530
AXIOMATIC CHARACTERIZATIONS......Page 532
RANDOM SEARCH......Page 533
INFORMATION THEORETIC METHODS IN STATISTICS......Page 534
REFERENCES......Page 536
CONTRIBUTION OF HUNGARIAN MATHEMATICIANS TO GAME THEORY......Page 540
REFERENCES......Page 550
A SHORT GUIDE TO THE HISTORY OF HUNGARY IN THE 20TH CENTURY......Page 552
1900-1920......Page 558
1920-1945......Page 560
1945-2000......Page 562
A SHORT NOTE ON THE USE OF NAMES OF PERSONS AND INSTITUTIONS, AND ON PRONUNCIATION:......Page 566
BIOGRAPHIES......Page 568
REFERENCES......Page 612
NAME INDEX......Page 626